It's pretty straightforward. You pay for access to the Internet through your ISP, which may be Comcast. Netflix pays for access to the Internet through their ISPs, although their service providers are probably a different tier than the consumer level service you're getting. The way it's supposed to work is that you're both connected to the Internet, so data you send between each other is covered by whatever plan you have with your ISP. What Comcast is doing here is double-dipping. They want to charge you for sending and receiving data to and from Netflix and also charge Netflix for sending and receiving data to and from you. The effect of this is that Netflix basically ends up paying twice for bandwidth. You may shrug your shoulders and say "why should I care", but who exactly do you think ultimately pays for this? The answer is that _you_ pay if you're a Comcast customer who uses Netflix (or any other service they manage to extort this way).
This is basically a telecom finding yet another way to charge hidden fees to customers. Ever actually look at the bill from pretty much any telecom such as Comcast? Ever look at the fees section? Where they directly charge you for all the taxes and other fees that anyone charges them? Things that every other business rolls into the final price as part of the cost of doing business but telecoms somehow get a pass to do? It allows them to lie to you about the price of your service when you sign up. Ever try to ask them in advance what your actual basic monthly bill will be when trying to order service and they can't or won't tell you? They're scum, plain and simple.
As businesses that require extensive, distributed infrastructure (mostly situated on property acquired through eminent domain, variances, etc. for the public good) telecoms tend to be what's referred to as "natural monopolies". As natural monopolies, they're meant to be heavily regulated since they generally can't even exist without massive exceptions and exceptional favors being granted to them. Trouble is, as vast, powerful monopolies, they distort the market they exist in and capture the regulatory system. They should be forced to act as non-profits and run as public utilities considering the massive abuses they perpetrate constantly. Trouble is, that won't fly well in the US where too many people are severely opposed to that kind of regulation of "private" industry, completely blind to the fact that the industry in question only exists because it gets the benefits of being a public institution without actually being one.